The Argentinian midfielder, who initially impressed during his loan spell at the London club, completed a permanent transfer worth around £9million on Tuesday.
"It's great," he said. "I was asking the two Daves (co-chairmen Sullivan and Gold) if they had sorted Lanzini out just a couple of weeks ago.
"He was outstanding until he got injured earlier this season. Then he came back and he and Dimitri Payet together are great.
"It's good to sort him, Payet and (Cheikhou) Kouyate out for the next few years."